Chronological Clustering Report

The following code digs into the chronological clustering of both the community size spectrum slopes, and the mean sizes across all years of the NMFS groundfish survey.

Data is prepared and updated using {targets} to ensure a consistent data state and a reproducible workflow.

Target Data

Data for the report comes directly from the {targets} workflow found in _targets.R.

####  Data  ####

####  Size Spectrum Targets 

# SS and manual bins together
withr::with_dir(rprojroot::find_root('_targets.R'), tar_load(size_spectrum_indices))   


####  OISST Data

# OISST for all the regions
withr::with_dir(rprojroot::find_root('_targets.R'), tar_load(regional_oisst))          


####  Size Data Targets

# 1. Biological data used as input
withr::with_dir(rprojroot::find_root('_targets.R'), tar_load(nefsc_1g))            

# 2. Mean sizes grouped on - yr, season, survey area, taxon group, fishery status
withr::with_dir(rprojroot::find_root('_targets.R'), tar_load(mean_individual_sizes))   

# 3. Mean sizes using same groupings as the size spectrum indices
withr::with_dir(rprojroot::find_root('_targets.R'), tar_load(mean_sizes_ss_groups))

Exploration of Abundance/Size Information

# Cut up discrete length and weight bins
nefsc_size_bins <- nefsc_1g %>% 
  mutate(
    length_bin = case_when(
      LngtClass <= 5   ~ "0 - 5cm",
      LngtClass <= 10  ~ "5 - 10cm",
      LngtClass <= 25  ~ "10 - 25cm",
      LngtClass <= 50  ~ "25 - 50cm",
      LngtClass <= 100 ~ "50 - 100cm",
      LngtClass >= 100 ~ ">= 100cm"),
    length_bin = factor(length_bin, levels = c(
      "0 - 5cm", "5 - 10cm", "10 - 25cm",
      "25 - 50cm", "50 - 100cm", ">= 100cm")))


# Weight bins
nefsc_size_bins <- nefsc_size_bins %>% 
  mutate(
    weight_bin = case_when(
      ind_weight_kg <= 0.001 ~ "0 - 1g",
      ind_weight_kg <= 0.005 ~ "1 - 5g",
      ind_weight_kg <= 0.010 ~ "5 - 10g",
      ind_weight_kg <= 0.050 ~ "10 - 50g",
      ind_weight_kg <= 0.100 ~ "50 - 100g",
      ind_weight_kg <= 0.500 ~ "100 - 500g",
      ind_weight_kg <= 1.000 ~ ".5 - 1kg",
      ind_weight_kg <= 5.000 ~ "1 - 5kg",
      ind_weight_kg <= 10.00 ~ "5 - 10kg",
      ind_weight_kg >= 10.00 ~ ">= 10kg" ),
    weight_bin = factor(weight_bin, levels = c(
      "0 - 1g", "1 - 5g", "5 - 10g", "10 - 50g",
      "50 - 100g", "100 - 500g", ".5 - 1kg",
      "1 - 5kg", "5 - 10kg", ">= 10kg")))


# Rename the functional groups
nefsc_size_bins <- nefsc_size_bins %>% 
  mutate(
    spec_class = case_when(
      spec_class == "gf"  ~ "Groundfish",
      spec_class == "pel" ~ "Pelagic",
      spec_class == "dem" ~ "Demersal",
      spec_class == "el"  ~ "Elasmobranch",
      spec_class == "<NA>" ~ "NA"
    ))

# Make regions go N->S
nefsc_size_bins <- nefsc_size_bins %>% 
  mutate(
    survey_area = factor(survey_area, levels = c("GoM", "GB", "SNE", "MAB")
    ))

Regional Differences

# Do some grouping
regional_totals <- nefsc_size_bins %>% 
  group_by(Year, survey_area) %>% 
  summarise(total_survey_catch = sum(Number),
            total_lw_bio = sum(sum_weight_kg),
            total_strat_abund = sum(expanded_abund_s),
            total_strat_lw_bio = sum(sum_weight_kg)) %>% 
  ungroup()

Length Bins

# Get fraction for different length/weight classes

# length bins
regional_lengths <- nefsc_size_bins %>% 
  group_by(Year, survey_area, length_bin) %>% 
  summarise(lenbin_survey_catch = sum(Number),
            lenbin_lw_bio       = sum(sum_weight_kg),
            lenbin_strat_abund  = sum(expanded_abund_s),
            lenbin_strat_lw_bio = sum(stratified_sum_bodymass)) %>% 
  left_join(regional_totals) %>% 
  mutate(
    perc_total_catch  = (lenbin_survey_catch - total_survey_catch) * 100,
    perc_lw_bio       = (lenbin_lw_bio - total_lw_bio) * 100,
    perc_strat_abund  = (lenbin_strat_abund - total_strat_abund) * 100,
    perc_strat_lw_bio = (lenbin_strat_lw_bio - total_strat_lw_bio) * 100)

# # Biomass from Survey using L-W
# ggplot(regional_lengths, aes(Year, lenbin_survey_catch, fill = length_bin)) +
#   geom_col(position = "stack") +
#   facet_wrap(~survey_area) +
#   scale_fill_gmri() +
#   scale_y_continuous(labels = comma_format()) +
#   labs(y = "Survey Catch",  
#        subtitle = "Total Survey Abundance",
#        x = "", 
#        fill = "Length Bin")



# Expected Biomass for Entire Survey Area
ggplot(regional_lengths, 
       aes(Year, lenbin_strat_abund, fill = length_bin)) +
  geom_col(position = "stack") +
  facet_wrap(~survey_area) +
  scale_fill_gmri() +
  scale_y_continuous(labels = comma_format()) +
  labs(y = "Total Predicted Abundance - Full Survey Area", 
       title = "Abundance",
       subtitle = "Expected Area-Stratified Abundance", 
       x = "", 
       fill = "Length Bin")

# # Biomass from Survey using L-W
# ggplot(regional_lengths, aes(Year, lenbin_lw_bio, fill = length_bin)) +
#   geom_col(position = "stack") +
#   facet_wrap(~survey_area) +
#   scale_fill_gmri() +
#   scale_y_continuous(labels = comma_format()) +
#   labs(y = "Survey Biomass (kg)", 
#        subtitle = "Survey Biomass",
#        x = "", 
#        fill = "Length Bin")



# Expected Biomass for Entire Survey Area
ggplot(regional_lengths, 
       aes(Year, lenbin_strat_lw_bio, fill = length_bin)) +
  geom_col(position = "stack") +
  facet_wrap(~survey_area) +
  scale_fill_gmri() +
  scale_y_continuous(labels = comma_format()) +
  labs(y = "Total Expected Biomass (kg) - Full Survey Area",  
       title = "Biomass",
       subtitle = "Expected Area-Stratified Biomass", 
       x = "", 
       fill = "Length Bin")+ theme(legend.position = "none")

Weight Bins

# weight bins
regional_weights <- nefsc_size_bins %>% 
  group_by(Year, survey_area, weight_bin) %>% 
  summarise(wtbin_survey_catch = sum(Number),
            wtbin_lw_bio       = sum(sum_weight_kg),
            wtbin_strat_abund  = sum(expanded_abund_s),
            wtbin_strat_lw_bio = sum(sum_weight_kg)) %>% 
  left_join(regional_totals) %>% 
  mutate(
    perc_total_catch  = (wtbin_survey_catch / total_survey_catch) * 100,
    perc_lw_bio       = (wtbin_lw_bio / total_lw_bio) * 100,
    perc_strat_abund  = (wtbin_strat_abund / total_strat_abund) * 100,
    perc_strat_lw_bio = (wtbin_strat_lw_bio / total_strat_lw_bio) * 100)

# # Biomass from Survey using L-W
# ggplot(regional_weights, aes(Year, wtbin_survey_catch, fill = weight_bin)) +
#   geom_col(position = "stack") +
#   facet_wrap(~survey_area) +
#   scale_fill_gmri() +
#   scale_y_continuous(labels = comma_format()) +
#   labs(y = "Survey Catch",  
#        subtitle = "Total Survey Abundance",
#        x = "", 
#        fill = "Length Bin")



# Expected Biomass for Entire Survey Area
ggplot(regional_weights, 
       aes(Year, wtbin_strat_abund, fill = weight_bin)) +
  geom_col(position = "stack") +
  facet_wrap(~survey_area) +
  scale_fill_gmri() +
  scale_y_continuous(labels = comma_format()) +
  labs(y = "Total Predicted Abundance - Full Survey Area", 
       title = "Abundance",
       subtitle = "Expected Area-Stratified Abundance" ,
       x = "",
       fill = "Weight Bin")

# # Biomass from Survey using L-W
# ggplot(regional_weights, 
#        aes(Year, wtbin_lw_bio, fill = weight_bin)) +
#   geom_col(position = "stack") +
#   facet_wrap(~survey_area) +
#   scale_fill_gmri() +
#   scale_y_continuous(labels = comma_format()) +
#   labs(y = "Survey Biomass (kg)", subtitle = "Survey Biomass", 
#        x = "", 
#        fill = "Length Bin")



# Expected Biomass for Entire Survey Area
ggplot(regional_weights, 
       aes(Year, wtbin_strat_lw_bio, fill = weight_bin)) +
  geom_col(position = "stack") +
  facet_wrap(~survey_area) +
  scale_fill_gmri() +
  scale_y_continuous(labels = comma_format()) +
  labs(y = "Total Expected Biomass (kg) - Full Survey Area", 
       title = "Biomass",
       subtitle = "Expected Area-Stratified Biomass", 
       x = "", 
       fill = "Weight Bin") + theme(legend.position = "none")

Seasonal Differences

# Do some grouping
seasonal_totals <- nefsc_size_bins %>% 
  group_by(Year, season) %>% 
  summarise(total_survey_catch = sum(Number),
            total_lw_bio = sum(sum_weight_kg),
            total_strat_abund = sum(expanded_abund_s),
            total_strat_lw_bio = sum(sum_weight_kg)) %>% 
  ungroup()

Length Bins

# Get fraction for different length/weight classes

# length bins
seasonal_lengths <- nefsc_size_bins %>% 
  group_by(Year, season, length_bin) %>% 
  summarise(lenbin_survey_catch = sum(Number),
            lenbin_lw_bio       = sum(sum_weight_kg),
            lenbin_strat_abund  = sum(expanded_abund_s),
            lenbin_strat_lw_bio = sum(sum_weight_kg)) %>% 
  left_join(seasonal_totals) %>% 
  mutate(
    perc_total_catch  = (lenbin_survey_catch - total_survey_catch) * 100,
    perc_lw_bio       = (lenbin_lw_bio - total_lw_bio) * 100,
    perc_strat_abund  = (lenbin_strat_abund - total_strat_abund) * 100,
    perc_strat_lw_bio = (lenbin_strat_lw_bio - total_strat_lw_bio) * 100)

# # Biomass from Survey using L-W
# ggplot(seasonal_lengths, aes(Year, lenbin_survey_catch, fill = length_bin)) +
#   geom_col(position = "stack") +
#   facet_wrap(~season) +
#   scale_fill_gmri() +
#   scale_y_continuous(labels = comma_format()) +
#   labs(y = "Survey Catch",  
#        subtitle = "Total Survey Abundance",
#        x = "", 
#        fill = "Length Bin")



# Expected Biomass for Entire Survey Area
ggplot(seasonal_lengths, 
       aes(Year, lenbin_strat_abund, fill = length_bin)) +
  geom_col(position = "stack") +
  facet_wrap(~season) +
  scale_fill_gmri() +
  scale_y_continuous(labels = comma_format()) +
  labs(y = "Total Predicted Abundance - Full Survey Area", 
       title = "Abundance",
       subtitle = "Expected Area-Stratified Abundance" ,
       x = "", 
       fill = "Length Bin")

# # Biomass from Survey using L-W
# ggplot(seasonal_lengths, 
#        aes(Year, lenbin_lw_bio, fill = length_bin)) +
#   geom_col(position = "stack") +
#   facet_wrap(~season) +
#   scale_fill_gmri() +
#   scale_y_continuous(labels = comma_format()) +
#   labs(y = "Survey Biomass (kg)", subtitle = "Survey Biomass",
#        x = "", 
#        fill = "Length Bin")



# Expected Biomass for Entire Survey Area
ggplot(seasonal_lengths, 
       aes(Year, lenbin_strat_lw_bio, fill = length_bin)) +
  geom_col(position = "stack") +
  facet_wrap(~season) +
  scale_fill_gmri() +
  scale_y_continuous(labels = comma_format()) +
  labs(y = "Total Expected Biomass (kg) - Full Survey Area", 
       title = "Biomass",
       subtitle = "Expected Area-Stratified Biomass", 
       x = "", 
       fill = "Length Bin") + theme(legend.position = "none")

Weight Bins

# weight bins
seasonal_weights <- nefsc_size_bins %>% 
  group_by(Year, season, weight_bin) %>% 
  summarise(wtbin_survey_catch = sum(Number),
            wtbin_lw_bio       = sum(sum_weight_kg),
            wtbin_strat_abund  = sum(expanded_abund_s),
            wtbin_strat_lw_bio = sum(sum_weight_kg)) %>% 
  left_join(seasonal_totals) %>% 
  mutate(
    perc_total_catch  = (wtbin_survey_catch / total_survey_catch) * 100,
    perc_lw_bio       = (wtbin_lw_bio / total_lw_bio) * 100,
    perc_strat_abund  = (wtbin_strat_abund / total_strat_abund) * 100,
    perc_strat_lw_bio = (wtbin_strat_lw_bio / total_strat_lw_bio) * 100)

# # Biomass from Survey using L-W
# ggplot(seasonal_weights, aes(Year, wtbin_survey_catch, fill = weight_bin)) +
#   geom_col(position = "stack") +
#   facet_wrap(~season) +
#   scale_fill_gmri() +
#   scale_y_continuous(labels = comma_format()) +
#   labs(y = "Survey Catch",  
#        subtitle = "Total Survey Abundance",
#        x = "", 
#        fill = "Length Bin")



# Expected Biomass for Entire Survey Area
ggplot(seasonal_weights, 
       aes(Year, wtbin_strat_abund, fill = weight_bin)) +
  geom_col(position = "stack") +
  facet_wrap(~season) +
  scale_fill_gmri() +
  scale_y_continuous(labels = comma_format()) +
  labs(y = "Total Predicted Abundance - Full Survey Area", 
       title = "Abundance",
       subtitle = "Expected Area-Stratified Abundance" ,
       x = "", 
       fill = "Weight Bin")

# # Biomass from Survey using L-W
# ggplot(seasonal_weights, 
#        aes(Year, wtbin_lw_bio, fill = weight_bin)) +
#   geom_col(position = "stack") +
#   facet_wrap(~season) +
#   scale_fill_gmri() +
#   scale_y_continuous(labels = comma_format()) +
#   labs(y = "Survey Biomass (kg)", subtitle = "Survey Biomass", 
#        x = "", 
#        fill = "Length Bin")



# Expected Biomass for Entire Survey Area
ggplot(seasonal_weights, 
       aes(Year, wtbin_strat_lw_bio, fill = weight_bin)) +
  geom_col(position = "stack") +
  facet_wrap(~season) +
  scale_fill_gmri() +
  scale_y_continuous(labels = comma_format()) +
  labs(y = "Total Expected Biomass (kg) - Full Survey Area",  
       title = "Biomass",
       subtitle = "Expected Area-Stratified Biomass", 
       x = "", 
       fill = "Weight Bin") + theme(legend.position = "none")

Functional Group Diffferences

# Do some grouping
fgroup_totals <- nefsc_size_bins %>% 
  group_by(Year, spec_class) %>% 
  summarise(total_survey_catch = sum(Number),
            total_lw_bio = sum(sum_weight_kg),
            total_strat_abund = sum(expanded_abund_s),
            total_strat_lw_bio = sum(sum_weight_kg)) %>% 
  ungroup()

# Display table of whichever specis fall into the categories
nefsc_size_bins %>% 
  distinct(SpecCode, scientific_name, spec_class) %>% 
  rename(`Common Name` = SpecCode, 
         `Scientific Name` = scientific_name,
         `Functional Group` = spec_class) %>% 
  arrange(`Functional Group`, `Common Name`) %>% 
  DT::datatable(filter = "top", rownames = FALSE)

Length Bins

# Get fraction for different length/weight classes

# length bins
fgroup_lengths <- nefsc_size_bins %>% 
  group_by(Year, spec_class, length_bin) %>% 
  summarise(lenbin_survey_catch = sum(Number),
            lenbin_lw_bio       = sum(sum_weight_kg),
            lenbin_strat_abund  = sum(expanded_abund_s),
            lenbin_strat_lw_bio = sum(sum_weight_kg)) %>% 
  left_join(fgroup_totals) %>% 
  mutate(
    perc_total_catch  = (lenbin_survey_catch - total_survey_catch) * 100,
    perc_lw_bio       = (lenbin_lw_bio - total_lw_bio) * 100,
    perc_strat_abund  = (lenbin_strat_abund - total_strat_abund) * 100,
    perc_strat_lw_bio = (lenbin_strat_lw_bio - total_strat_lw_bio) * 100)

# # Biomass from Survey using L-W
# ggplot(fgroup_lengths, aes(Year, lenbin_survey_catch, fill = length_bin)) +
#   geom_col(position = "stack") +
#   facet_wrap(~spec_class) +
#   scale_fill_gmri() +
#   scale_y_continuous(labels = comma_format()) +
#   labs(y = "Survey Catch",  
#        subtitle = "Total Survey Abundance",
#        x = "", 
#        fill = "Length Bin")



# Expected Biomass for Entire Survey Area
ggplot(fgroup_lengths, 
       aes(Year, lenbin_strat_abund, fill = length_bin)) +
  geom_col(position = "stack") +
  facet_wrap(~spec_class) +
  scale_fill_gmri() +
  scale_y_continuous(labels = comma_format()) +
  labs(y = "Total Predicted Abundance - Full Survey Area", 
       title = "Abundance",
       subtitle = "Expected Area-Stratified Abundance" ,
       x = "", 
       fill = "Length Bin")

# # Biomass from Survey using L-W
# ggplot(fgroup_lengths, 
#        aes(Year, lenbin_lw_bio, fill = length_bin)) +
#   geom_col(position = "stack") +
#   facet_wrap(~spec_class) +
#   scale_fill_gmri() +
#   scale_y_continuous(labels = comma_format()) +
#   labs(y = "Survey Biomass (kg)", subtitle = "Survey Biomass", 
#        x = "", 
#        fill = "Length Bin")



# Expected Biomass for Entire Survey Area
ggplot(fgroup_lengths, 
       aes(Year, lenbin_strat_lw_bio, fill = length_bin)) +
  geom_col(position = "stack") +
  facet_wrap(~spec_class) +
  scale_fill_gmri() +
  scale_y_continuous(labels = comma_format()) +
  labs(y = "Total Expected Biomass (kg) - Full Survey Area",  
       title = "Biomass",
       subtitle = "Expected Area-Stratified Biomass", 
       x = "", 
       fill = "Length Bin")

Weight Bins

# weight bins
fgroup_weigths <- nefsc_size_bins %>% 
  group_by(Year, spec_class, weight_bin) %>% 
  summarise(wtbin_survey_catch = sum(Number),
            wtbin_lw_bio       = sum(sum_weight_kg),
            wtbin_strat_abund  = sum(expanded_abund_s),
            wtbin_strat_lw_bio = sum(sum_weight_kg)) %>% 
  left_join(fgroup_totals) %>% 
  mutate(
    perc_total_catch  = (wtbin_survey_catch / total_survey_catch) * 100,
    perc_lw_bio       = (wtbin_lw_bio / total_lw_bio) * 100,
    perc_strat_abund  = (wtbin_strat_abund / total_strat_abund) * 100,
    perc_strat_lw_bio = (wtbin_strat_lw_bio / total_strat_lw_bio) * 100)

# # Biomass from Survey using L-W
# ggplot(fgroup_weigths, aes(Year, wtbin_survey_catch, fill = weight_bin)) +
#   geom_col(position = "stack") +
#   facet_wrap(~spec_class) +
#   scale_fill_gmri() +
#   scale_y_continuous(labels = comma_format()) +
#   labs(y = "Survey Catch",  
#        subtitle = "Total Survey Abundance",
#        x = "", 
#        fill = "Weight Bin")



# Expected Biomass for Entire Survey Area
ggplot(fgroup_weigths, 
       aes(Year, wtbin_strat_abund, fill = weight_bin)) +
  geom_col(position = "stack") +
  facet_wrap(~spec_class) +
  scale_fill_gmri() +
  scale_y_continuous(labels = comma_format()) +
  labs(y = "Total Predicted Abundance - Full Survey Area", 
       title = "Abundance",
       subtitle = "Expected Area-Stratified Abundance", 
       x = "", 
       fill = "Weight Bin")

# # Biomass from Survey using L-W
# ggplot(fgroup_weigths, 
#        aes(Year, wtbin_lw_bio, fill = weight_bin)) +
#   geom_col(position = "stack") +
#   facet_wrap(~spec_class) +
#   scale_fill_gmri() +
#   scale_y_continuous(labels = comma_format()) +
#   labs(y = "Survey Biomass (kg)", 
#        subtitle = "Survey Biomass", 
#        x = "", 
#        fill = "Weight Bin")



# Expected Biomass for Entire Survey Area
ggplot(fgroup_weigths, 
       aes(Year, wtbin_strat_lw_bio, fill = weight_bin)) +
  geom_col(position = "stack") +
  facet_wrap(~spec_class) +
  scale_fill_gmri() +
  scale_y_continuous(labels = comma_format()) +
  labs(y = "Total Expected Biomass (kg) - Full Survey Area",  
       title = "Biomass",
       subtitle = "Expected Area-Stratified Biomass", 
       x = "", 
       fill = "Weight Bin")

Community Size Spectra

Community size spectrum slopes were estimated using 2 methods for comparison, using a minimum individual biomass of 1 gram, and using area stratified abundances.

The first was using the methods of the {sizeSpectra} package which were shown to be the most accurate when using simulated data.

The second method uses binned abundances, with bins of width 0.5 on a log10 scale, so 10^0 - 10^0.5 etc. These bins were then normalized by dividing the abundances by the bin width to account for the increasing bin size.

Results from Both Methods

# Pull the group ID for the slopes grouped on year, season, and region
warmem_group_slopes <- size_spectrum_indices %>% 
  filter(`group ID`== "single years * season * region") %>% 
  mutate(season = fct_rev(season),
         survey_area = factor(survey_area, 
                              levels = c("GoM", "GB", "SNE", "MAB")),
         yr = as.numeric(as.character(Year)))

The Bodymass Data to Match

# Do some grouping
warmem_totals <- nefsc_size_bins %>% 
  group_by(Year, survey_area, season) %>% 
  summarise(total_survey_catch = sum(Number),
            total_lw_bio = sum(sum_weight_kg),
            total_strat_abund = sum(expanded_abund_s),
            total_strat_lw_bio = sum(sum_weight_kg)) %>% 
  ungroup()


# weight bins
warmem_weights <- nefsc_size_bins %>% 
  group_by(Year, survey_area, season, weight_bin) %>% 
  summarise(wtbin_survey_catch = sum(Number),
            wtbin_lw_bio       = sum(sum_weight_kg),
            wtbin_strat_abund  = sum(expanded_abund_s),
            wtbin_strat_lw_bio = sum(sum_weight_kg)) %>% 
  left_join(warmem_totals) %>% 
  mutate(
    perc_total_catch  = (wtbin_survey_catch / total_survey_catch) * 100,
    perc_lw_bio       = (wtbin_lw_bio / total_lw_bio) * 100,
    perc_strat_abund  = (wtbin_strat_abund / total_strat_abund) * 100,
    perc_strat_lw_bio = (wtbin_strat_lw_bio / total_strat_lw_bio) * 100)

# # Expected Abundance for Entire Survey Area
# ggplot(warmem_weights, 
#        aes(Year, wtbin_strat_abund, fill = weight_bin)) +
#   geom_col(position = "stack") +
#   facet_grid(season~survey_area) +
#   scale_fill_gmri() +
#   scale_y_continuous(labels = comma_format()) +
#   labs(y = "Total Predicted Abundance - Full Survey Area", 
#        subtitle = "Expected Area-Stratified Abundance" ,
#        x = "",
#        fill = "Length Bin")

# Expected Biomass for Entire Survey Area
ggplot(warmem_weights, 
       aes(Year, wtbin_strat_lw_bio, fill = weight_bin)) +
  geom_col(position = "stack") +
  facet_grid(season~survey_area) +
  scale_fill_gmri() +
  scale_y_continuous(labels = comma_format()) +
  labs(y = "Total Expected Biomass (kg) - Full Survey Area",  
       title = "Biomass",
       subtitle = "Expected Area-Stratified Biomass", 
       x = "", 
       fill = "Length Bin")

Edwards Methodology

The Edwards methodology differs from the other methods for estimating size spectra by avoiding the subjective decisions around how to bin data prior to fitting the log-linear regression.

Instead, Edwards uses the individual size distributions (how many individuals of any given length/weight). Abundances are totaled into discrete size bins based on expected biomass at length and length + 1, and individuals that fall within those bins are totaled to get abundances across a continuous distribution of individual bodymass.

The next difference is that the individual body size data is presumed to follow a bounded power-law distribution, with a minimum and maximum body size. Using the individual size data, maximum likelihood estimation is used to solve for the parameter (b) that minimizes the negative log-likelihood.

Long-Term Patterns

# Plot the sizeSpectra slopes
(ss_patterns <- warmem_group_slopes %>% 
  ggplot(aes(yr, b, color = survey_area)) +
  geom_line(aes(group = survey_area)) +
  geom_point(alpha = 0.6) +
  facet_grid(season~survey_area) +
  scale_color_gmri() +
  labs(x = "", 
       y = "Size Spectrum Slope (b)", 
       color = "",
       title = "Results from Area-Stratified Abundance - Edwards Method") 
)